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Topic: Which Polynomial?
Replies: 28   Last Post: Jul 27, 2006 3:13 PM

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Victor Steinbok

Posts: 1,580
Registered: 12/3/04
Re: Which Polynomial?
Posted: Jul 31, 2005 1:07 AM
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At 07:42 PM 7/30/2005, Kirby Urner wrote:
> > Well, if we are going to split hairs, it's "phee",
> > but who cares!
> >

>In English we say fie, as in fee FIE foe fum.

My dictionary says otherwise.

> > The two roots (actually, halves of the two
> > roots, if I recall correctly) generate the Fibonacci
> > sequence.

>The phi sequence is both geometric and recursively additive.
>The usual thing we do with the Fibonacci sequence is show how the ratio
>(F[n+1]/F[n]) --> phi as n --> infinity, where F[n+1] and F[n] are
>successive terms in this series.

No, no, Kirby. Look at the sequence f1^n+f2^n. Every recursively-generated
sequence has a generating polynomial. f1 and f2 are the two roots.

>Math-through-storytelling: part of what we're doing is passing on a
>history, a "where we've been" story. It's not like history is
>irrelevant. On the other hand, phi to this day has geometric importance
>-- its value undimished with time (like gold).

Weeellll... It's a stretch. We no longer build Parthenons.

>phi is an idea and is irreplacable.

In itself--yes. But not in the curriculum.

>I'd think phi, pi and e we could at least agree on, though we might take
>different approaches in introducing them.

These are not in the same category. One is essential at an elementary
level, the other--a bit later. The third is a mere curiosity--a bump on a
path to knowledge.

>It's implicit in writing curriculum that one is saying something like
>"follow me" -- and then only some do, maybe none. That's a given.

Really? You obviously are not a member of Mathematically Erect. Also, see
the comment about mx+b above--the notation became a convention because it
was used in a popular book, not because it has any meaning or convenience.

>However, within the rhetorical conceit of offering leadership, it behooves
>me to be persuasive, to exercise whatever leadership experience and
>qualities I possess.

If at first you don't succeed, try and try again...

>So: NCLB people, listen up, we're going to push Phi (FIE) and we're going
>to do it in connection with solving a Polynomial. This will provide
>positive reinforcement for (a) the quadratic formula (b) completing the
>square, plus it'll lead to connected topics such as: Fibonacci numbers,
>sequences, and five-fold symmetry ala pentagons.

The NCLB people don't give a rat's ass!


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